"... nothing worked that depends on the ignition switch being on, but the headlights work.".

I would check the connections inside the small Black Plastic terminal box on the left fender rail (near the Hi/Lo headlight relay - also a suspect).

Power to the terminal box comes straight from the battery, and goes straight (unfused) to the light switch–so the lights worked. But another terminal goes to Ignition Switch terminal 30. Loss of power there would kill everything.

Be sure to remove the battery Negative cable when you go in to check and clean those terminals.

I can't explain the tie-in to the Head Light operation.
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Bruce Young
'93 940-NA (current) — 240s (one V8) — 140s — 122s — since '63.